Most stringent bounds on the probability of the union and intersection of m events for systems partially specified by s1, s2, …sk, 2 ≦ k < m

Abstract

For dependent probability systems of m events partially specified by the quantities Sv, the sum of the probabilities of each of the combinations of v events, v = 1, 2, …, 2 ≦ k < m; this paper develops the most stringent upper and lower bounds on P1, the probability of the union of the m events; and on P[m], the probability of the simultaneous occurrence of the m events.